Analysis of zz-www.sudokuwiki.org-0021-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=21

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=21

position: .34....1...26.........9......6....258...3...9.7....4.8....5...3.....79...6....24. initial

Autosolve

position: 934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I3: 4,7 => CTR => I3: 2
* DIS # B5: 1,5 => CTR => B5: 2,4
* PRF # H7: 6,7 => SOL
* DIS # E8: 1,8 => CTR => E8: 2,4,6
* PRF # D9: 1,8 => SOL
* DIS # F9: 1,8 => CTR => F9: 3,9
* DIS # C9: 1,8 => CTR => C9: 3,5,7,9
* DIS # E8: 2,4,8 => CTR => E8: 1,6
* DIS # A9: 1,7 => CTR => A9: 3,5
* CNT   9 HDP CHAINS /  32 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # I3: 4,7 => CTR => I3: 2
* DIS I3: 2 # B5: 1,5 => CTR => B5: 2,4
* DIS I3: 2 + B5: 2,4 # A6: 1,5 => CTR => A6: 2,3
* PRF I3: 2 + B5: 2,4 + A6: 2,3 # H7: 6,7 => SOL
* STA I3: 2 + B5: 2,4 + A6: 2,3 + H7: 6,7
* CNT   4 HDP CHAINS /  11 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

.34....1...26.........9......6....258...3...9.7....4.8....5...3.....79...6....24. initial
934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24. autosolve
934825716182673594657491382396748125841532679275916438719254863428367951563189247 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
I2: 4,7
C5: 1,5
H5: 6,7
H6: 3,6
E9: 1,8
I8: 1,6
I9: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,G5: 1.. / G4 = 1  =>  9 pairs (_) / G5 = 1  => 10 pairs (_)
I8,I9: 1.. / I8 = 1  =>  0 pairs (*) / I9 = 1  =>  0 pairs (X)
I1,I3: 2.. / I1 = 2  =>  0 pairs (X) / I3 = 2  =>  7 pairs (_)
B5,A6: 2.. / B5 = 2  =>  8 pairs (_) / A6 = 2  =>  8 pairs (_)
G4,H6: 3.. / G4 = 3  =>  0 pairs (X) / H6 = 3  =>  8 pairs (_)
F2,G2: 3.. / F2 = 3  =>  7 pairs (_) / G2 = 3  => 11 pairs (_)
A4,G4: 3.. / A4 = 3  =>  8 pairs (_) / G4 = 3  =>  0 pairs (X)
H3,H6: 3.. / H3 = 3  =>  0 pairs (X) / H6 = 3  =>  8 pairs (_)
I2,I3: 4.. / I2 = 4  =>  7 pairs (_) / I3 = 4  =>  0 pairs (X)
A9,C9: 5.. / A9 = 5  =>  8 pairs (_) / C9 = 5  =>  0 pairs (X)
G1,I1: 6.. / G1 = 6  =>  0 pairs (X) / I1 = 6  =>  0 pairs (_)
F7,E8: 6.. / F7 = 6  =>  0 pairs (X) / E8 = 6  =>  0 pairs (_)
E8,I8: 6.. / E8 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
E6,E8: 6.. / E6 = 6  =>  0 pairs (X) / E8 = 6  =>  0 pairs (_)
I1,I8: 6.. / I1 = 6  =>  0 pairs (*) / I8 = 6  =>  0 pairs (X)
A2,C3: 7.. / A2 = 7  => 11 pairs (_) / C3 = 7  => 11 pairs (_)
G7,H7: 8.. / G7 = 8  =>  0 pairs (*) / H7 = 8  =>  0 pairs (X)
H3,H7: 8.. / H3 = 8  =>  0 pairs (*) / H7 = 8  =>  0 pairs (X)
B4,C6: 9.. / B4 = 9  =>  7 pairs (_) / C6 = 9  =>  9 pairs (_)
B4,B7: 9.. / B4 = 9  =>  7 pairs (_) / B7 = 9  =>  9 pairs (_)
* DURATION: 0:00:26.776714  START: 03:47:33.123061  END: 03:47:59.899775 2017-05-01
* CP COUNT: (20)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E9,H5,H6,I2,I8,I9)
* 934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24.
* PAIR I2: 4,7 BLK 3
I3: 4,7,2                                # reduction candidate for 4,7
I3: 4,7 => CTR
* 934.7.612.826...9.6...9..8.3.6....258...3..69.7..6.438....56873.18327956.6398.241
I3: 2                                    #  7 pairs
* PAIR I2: 4,7 ROW 2
E2: 4,7,1,8                              # reduction candidate for 4,7
E2: 4,7                                  # 12 pairs
E2: 1,8                                  # 11 pairs
* PAIR C5: 1,5 BLK 4
B5: 1,5,2,4                              # reduction candidate for 1,5
B5: 1,5 => CTR
* 934.2.617..26...946...9..82346...1258...3.769279.6.43849..5687312..47956.6....241
B5: 2,4                                  #  9 pairs
A6: 1,5,2,3                              # reduction candidate for 1,5
A6: 1,5                                  # 12 pairs
C6: 1,5,3,9                              # reduction candidate for 1,5
C6: 1,5                                  # 15 pairs
* PAIR C5: 1,5 ROW 5
D5: 1,5,2,4,7                            # reduction candidate for 1,5
D5: 1,5                                  # 13 pairs
F5: 1,5,2,4,6                            # reduction candidate for 1,5
F5: 1,5                                  # 13 pairs
* PAIR C5: 1,5 COL C
C3: 1,5,7,8                              # reduction candidate for 1,5
C3: 1,5                                  # 15 pairs
C9: 1,5,3,7,8,9                          # reduction candidate for 1,5
C9: 1,5                                  # 12 pairs
* PAIR H5: 6,7 BLK 6
G5: 6,7,1                                # reduction candidate for 6,7
G5: 1                                    # 10 pairs
G5: 6,7                                  #  9 pairs
* PAIR H5: 6,7 COL H
H7: 6,7,8                                # reduction candidate for 6,7
H7: 6,7 => SOLVED
* 934825716182673594657491382396748125841532679275916438719254863428367951563189247
H7: 8                                    # 10 pairs
* PAIR E9: 1,8 BLK 8
D8: 1,8,2,3,4                            # reduction candidate for 1,8
D8: 1,8                                  # 13 pairs
E8: 1,8,2,4,6                            # reduction candidate for 1,8
E8: 1,8 => CTR
* 934.2.617.8267..94657.943823.6.4..2584..32.6927..6.438....56873..8..7956.6..8.241
E8: 2,4,6                                #  7 pairs
D9: 1,8,3,9                              # reduction candidate for 1,8
D9: 1,8 => SOLVED
* 934825716182673594657491382396748125841532679275916438719254863428367951563189247
D9: 3,9                                  #  8 pairs
F9: 1,8,3,9                              # reduction candidate for 1,8
F9: 1,8 => CTR
* 934.2.716..2673.946.7194..2..6748.2584.23..7927.5194687.9452683428367951.6.981247
F9: 3,9                                  #  8 pairs
* PAIR E9: 1,8 ROW 9
C9: 1,8,3,5,7,9                          # reduction candidate for 1,8
C9: 1,8 => CTR
* 934.2..16..267..946.7.9...2..6.4..2584..3..7927..1.4.87...5...34...6795156..8.247
C9: 3,5,7,9                              #  7 pairs
* PAIR E9: 1,8 COL E
E2: 1,8,4,7                              # reduction candidate for 1,8
E2: 1,8                                  # 11 pairs
E4: 1,8,4,7                              # reduction candidate for 1,8
E4: 1,8                                  # 15 pairs
* PAIR I8: 1,6 ROW 8
E8: 1,6,2,4,8                            # reduction candidate for 1,6
E8: 2,4,8 => CTR
* 934...61..826...9.6...9..8.3.6....258...3..69.7..6.438....56873..83.7956.6398.241
E8: 1,6                                  #  9 pairs
* PAIR I9: 1,7 ROW 9
A9: 1,7,3,5                              # reduction candidate for 1,7
A9: 1,7 => CTR
* 934....1.7.26...946.8.9..72346.7.125821.3.769579...438.97.5.683.83..795.165.8.247
A9: 3,5                                  #  8 pairs
C9: 1,7,3,5,8,9                          # reduction candidate for 1,7
C9: 1,7                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0021-base-pr-000.dot
* REASONING
* DIS # I3: 4,7 => CTR => I3: 2
* DIS # B5: 1,5 => CTR => B5: 2,4
* PRF # H7: 6,7 => SOL
* DIS # E8: 1,8 => CTR => E8: 2,4,6
* PRF # D9: 1,8 => SOL
* DIS # F9: 1,8 => CTR => F9: 3,9
* DIS # C9: 1,8 => CTR => C9: 3,5,7,9
* DIS # E8: 2,4,8 => CTR => E8: 1,6
* DIS # A9: 1,7 => CTR => A9: 3,5
* CNT   9 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E9,H5,H6,I2,I8,I9)
* 934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24.
* PAIR I2: 4,7 BLK 3
I3: 4,7,2                                # reduction candidate for 4,7
I3: 4,7 => CTR
* 934.7.612.826...9.6...9..8.3.6....258...3..69.7..6.438....56873.18327956.6398.241
* PAIR C5: 1,5 BLK 4
B5: 1,5,2,4                              # reduction candidate for 1,5
B5: 1,5 => CTR
* 934.2.617..26...946...9..82346....258...32.69279.6.43849.2568731...47956.6..8.241
A6: 1,5,2,3                              # reduction candidate for 1,5
A6: 1,5 => CTR
* 934.2.617..26...946...9..82346....2582..3..69.79.6243849.2568732.8.47956.6..8.241
C6: 1,5,3,9                              # reduction candidate for 1,5
C6: 1,5                                  # 15 pairs
* RESTART
* PAIR C5: 1,5 BLK 4
C6: 1,5,3,9                              # reduction candidate for 1,5
C6: 1,5                                  # 15 pairs
C6: 3,9                                  # 12 pairs
* PAIR C5: 1,5 ROW 5
D5: 1,5,2,4,7                            # reduction candidate for 1,5
D5: 1,5                                  # 21 pairs
F5: 1,5,2,4,6                            # reduction candidate for 1,5
F5: 1,5                                  # 23 pairs
* PAIR H5: 6,7 BLK 6
G5: 6,7,1                                # reduction candidate for 6,7
G5: 6,7                                  # 19 pairs
G5: 1                                    # 11 pairs
* PAIR H5: 6,7 COL H
H7: 6,7,8                                # reduction candidate for 6,7
H7: 6,7 => SOLVED
* 934825716182673594657491382396748125841532679275916438719254863428367951563189247
* DURATION: 0:00:11.589824  START: 03:48:22.470459  END: 03:48:34.060283 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0021-base-pr-001.dot
* REASONING
* DIS # I3: 4,7 => CTR => I3: 2
* DIS I3: 2 # B5: 1,5 => CTR => B5: 2,4
* DIS I3: 2 + B5: 2,4 # A6: 1,5 => CTR => A6: 2,3
* PRF I3: 2 + B5: 2,4 + A6: 2,3 # H7: 6,7 => SOL
* STA I3: 2 + B5: 2,4 + A6: 2,3 + H7: 6,7
* CNT   4 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=21

Solution

position: 934825716182673594657491382396748125841532679275916438719254863428367951563189247 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* DIS # I3: 4,7 => CTR => I3: 2
* INC # I3: 2 => UNS
* INC # E2: 4,7 => UNS
* INC # E2: 1,8 => UNS
* DIS # B5: 1,5 => CTR => B5: 2,4
* INC # B5: 2,4 => UNS
* INC # A6: 1,5 => UNS
* INC # C6: 1,5 => UNS
* INC # D5: 1,5 => UNS
* INC # F5: 1,5 => UNS
* INC # C3: 1,5 => UNS
* INC # C9: 1,5 => UNS
* INC # G5: 6,7 => UNS
* INC # G5: 1 => UNS
* PRF # H7: 6,7 => SOL
* INC # H7: 8 => UNS
* INC # D8: 1,8 => UNS
* DIS # E8: 1,8 => CTR => E8: 2,4,6
* INC # E8: 2,4,6 => UNS
* PRF # D9: 1,8 => SOL
* INC # D9: 3,9 => UNS
* DIS # F9: 1,8 => CTR => F9: 3,9
* INC # F9: 3,9 => UNS
* DIS # C9: 1,8 => CTR => C9: 3,5,7,9
* INC # C9: 3,5,7,9 => UNS
* INC # E2: 1,8 => UNS
* INC # E4: 1,8 => UNS
* INC # E8: 1,6 => UNS
* DIS # E8: 2,4,8 => CTR => E8: 1,6
* DIS # A9: 1,7 => CTR => A9: 3,5
* INC # A9: 3,5 => UNS
* INC # C9: 1,7 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # I3: 4,7 => CTR => I3: 2
* DIS I3: 2 # B5: 1,5 => CTR => B5: 2,4
* DIS I3: 2 + B5: 2,4 # A6: 1,5 => CTR => A6: 2,3
* INC I3: 2 + B5: 2,4 + A6: 2,3 # C6: 1,5 => UNS
* INC I3: 2 + B5: 2,4 + A6: 2,3 # C6: 1,5 => UNS
* INC I3: 2 + B5: 2,4 + A6: 2,3 # C6: 3,9 => UNS
* INC I3: 2 + B5: 2,4 + A6: 2,3 # D5: 1,5 => UNS
* INC I3: 2 + B5: 2,4 + A6: 2,3 # F5: 1,5 => UNS
* INC I3: 2 + B5: 2,4 + A6: 2,3 # G5: 6,7 => UNS
* INC I3: 2 + B5: 2,4 + A6: 2,3 # G5: 1 => UNS
* PRF I3: 2 + B5: 2,4 + A6: 2,3 # H7: 6,7 => SOL
* STA I3: 2 + B5: 2,4 + A6: 2,3 + H7: 6,7
* CNT  11 HDP CHAINS /  11 HYP OPENED